If an expensive, direct measurement is infeasible, measurements can be made more indirectly in test fixtures.
Direct operation: kill DC bus, and measure the high side directly. The output is at GND, so it can be probe-grounded without issue. Additional tests can also be made (e.g., active load on the local supply to test for load capability and (differential) transient immunity, etc.) This does not subject the driver to switching noise.
Ambient noise: set up a transient generator, and couple it into the driver in various ways (without compromising the probed signal quality). Example: high voltage step or impulse into a wire or plate, placed near the driver. This tests induced electric field noise.
Signal side noise: if the driver is isolated, set up some basic stimulus (e.g., a 555 to generate waveforms, a battery to supply power, etc.) on the isolated signal-input side. Pack it all into a metal box, and drive the box (ground) with the transient generator. Tie the high side driver to ground plane. This tests the isolation barrier for transient immunity, dV/dt, that sort of thing. Don't forget to check with respect to phase of the driving signal, in case it's prone to hiccups coincident with its own switching.
If the driver is bootstrap, probably ignore this step. (Some signal-to-power-ground noise can still be tested on these, but also you have a fully qualified IC on your hands, so these tests probably aren't a big deal anyway.)
Power side noise: this gets harder to test; an isolated probe is hard to avoid. An option is to tie the high side driver into ground plane, and subject the inverter pins to transients. Probe signal quality can be okay thanks to the ground plane. Grounding and shielding must be very good. This tests magnetic immunity.
This combination of tests, still misses edge cases with combinations of electric and magnetic noise, and has to make some assumptions about the layout and grounding.
You might also consider filling in for a probe, with some cute logic circuits to monitor levels or state instead. Example: if you are concerned about generating runt pulses of either polarity, or interruptions to steady levels, you can use a pulse detector and latch that into an LED. As you increase stimulus (load voltage or current, or one of the above transient tests say), if at some point the light turns on, you can set up a more specific test to recreate the symptom in a more controlled environment.
That said, several of these tests may be of interest in general, as:
1. Low side drivers aren't generally subjected to such fields, so if their layouts or circuits differ, potential problems may go unnoticed.
2. You can test to much higher voltages, or dV/dt, than the application requires. With a suitable transient generator, you might test the circuit to malfunction, and see its true limits; now you have a measure of how much guard band you have above normal operation.
3. You can test with more waveforms (steps, impulses, CW..), and at more frequencies (PRF, modulation, burst patterns, etc.), than the inverter itself is likely to generate.
One last thing -- note that I haven't even mentioned the gate drive waveforms themselves. This is a design quantity; you should have very little reason to measure it specifically! It depends on the driver (voltage, current and speed), transistor (gate charge, resistance), load (drain/collector voltage Miller effect, and source/emitter degeneration), and how they are connected (likely the gate connection will have a much higher TL impedance than the driver, so manifests as simple stray inductance). The only parameter which varies with operation, is the load, and you can measure that on the low side, and assume it is representative for all channels -- again, assuming the layouts are consistent and well behaved.
Tim